Topological origins of bound states in the continuum for systems with conical intersections

TL;DR

This paper investigates the topological and geometric phase effects associated with conical intersections in vibronic models and demonstrates that these phases are crucial for the emergence of bound states in the continuum.

Contribution

It reveals the essential role of geometric phases in the formation of BSCs in systems with conical intersections, extending previous models.

Findings

Geometric phase is crucial for BSC emergence.

Modifications removing GP eliminate BSCs.

Adding GP effects can restore BSCs.

Abstract

Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett. 90, 013001 (2003)]. It was also found that these states are destroyed within the Born-Oppenheimer approximation (BOA). We investigate whether a nontrivial topological or geometric phase (GP) associated with the CI is responsible for BSCs. To address this question we explore modifications of the original two-dimensional two-state linear vibronic coupling model supporting BSCs. These modifications either add GP effects after the BOA or remove the GP within a two-state problem. Using the stabilization graph technique we shown that the GP is crucial for emergence of BSCs.